Special Issue on Virtual Knot TheoryNo Access

RIBBON TORUS KNOTS PRESENTED BY VIRTUAL KNOTS WITH UP TO FOUR CROSSINGS

ATSUSHI ICHIMORI

Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

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and

TAIZO KANENOBU

Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

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https://doi.org/10.1142/S0218216512400056Cited by:5 (Source: Crossref)

Abstract

A ribbon torus knot embedded in the 4-space is presented by a welded virtual knot through the tube operation due to Shin Satoh. We make an attempt of classification of ribbon torus knots presented by virtual knots with up to four crossings, where we use the list of virtual knots enumerated by Jeremy Green. We mainly investigate the groups of virtual knots.

Keywords:

AMSC: 57M25

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